The police force in question is the Metropolitan Police Service. Wikipedia does note that it combined with an earlier police force called River Thames Marine Police Force, but they were founded in 1798.
I think WP means police as Police as we know today. The watchmen system exists since the early civilizations.
I noticed you specified European, but I could provide some information on early proto-police forces in the United States if that would be of interest. Modern police forces emerged in the US almost simultaneously with those in Europe.
So wouldn't that mean that the first police force was actually founded in 1798?
Apologies if I'm incorrect in suggesting this, but wouldn't the Cohortes urbanae of Augustan Rome technically be the first police force in Europe?
In actuality the first police force in Europe was that of Glasgow. The Glasgow City Police were given jurisdiction by the Glasgow Police Act, passed in 1800, 29 years before the process was replicated for the Met. The Met even released a statement renouncing their claim to the title of oldest police force in the world to Glasgow. (1)
Scotland may be the place to look for a history of 18th century policing. Edinburgh and Glasgow both had established traditions for centralised policing of urban areas. In 1779 James Buchanan became the first Inspector of a publicly funded police force, although the project failed due to a lack of interest and incentive for Westminister.(2)
The Edinburgh Town Guard has an even longer history, dating back to 1513, (3) fulfilling your criteria for 17th century policing, and even further! At the time Edinburgh's Old Town was one of the most dense areas in Europe, with buildings being constructed directly on top one another creating myriad alleys that provided a backdrop for crime.
There are two incarnations of the Town Guard. The Battle of Flodden in 1513 necessitated restoring order in the beseiged city. The Flodden Wall was built around the city to fortify it against further attack and to increase public order, and Guard was first founded to patrol the wall and serve as a garrison. Every fourth citizen would take watch.
From 1679 onwards, this changed dramatically. The second incarnation of the Town/City Guard had a distinctly military feel, drilling and marching in public on the Royal Mile to create a spectacle for the public and a deterrence to criminals. Their training was similar to contemporary militaries and their recruits were drawn from veteran ranks and Highlander clans. Often they were used as an auxiliary militia, such as in the Jacobite Rebellion. (4)
During a public hanging in 1736, a riot broke out and a mob formed. The City Guard were armed and fired a volley above the heads of the crowd, hitting residents of the tenements surrounding and further angering the crowd. After the captain in charge was imprisoned, and a commission was ordered for an increase in the number of guards, public sentiment was soured against him. A crowd of thousand gathered to prevent him from being provided safety to safety and broke into the prison. They removed Captain John Porteous and took him to the site of the public hanging the be lynched.
The site upon which the old prison known as the Tollbooth stood is a local attraction in Edinburgh known as the Heart of Midlothian, referring to a Sir Walter Scott book on the Porteous Riots. Locals spit on the heart, either in disdain or out of respect for authority, and out of reverence for those who were executed.
The Edinburgh Town Guard was probably the oldest surviving example of pre-metropolitan law enforcement when it was disbanded in 1817 due to institutional failure, including numerous incidents of public resistance being met with brutal force. The Glasgow and Metropolitan Police Acts were of a new breed of publicly funded, socially orientated law enforcement that still persists today.
The continued focus on the Met and their predecessor organisation the Bow Street Runners as the "foundation" of modern policing is a result of unfortunate London-centrism within the UK and also outside of it.
I hope this has been adequate for a top level response, it is my first time off the blocks.
Sources (1)http://www.sln.law.ed.ac.uk/2008/07/05/gonnae-nae-dae-that-glesca-polis-see-off-metropolitan-untruths/ http://www.electricscotland.com/history/glasgow/anec132.htm (2)http://www.scottish-places.info/features/featurefirst17366.html http://www.glasgowlife.org.uk/libraries/the-mitchell-library/archives/collections/police-archives/pages/default.aspx (2)http://georgianedinburgh.blogspot.co.uk/2011/09/edinburghs-town-guard.html (3)http://www.edinburghcityguard.org.uk/guard-history/4571951145